Strategies for the synthesis of crystalline, absorbable, glycolide-based polymers based primarily on glycolide for the production of medical devices that exhibit in-use dimensional stability have been limited to (1) random copolymers with at least 80 percent of their chains derived from glycolide, as in the case of 10:90 poly(l-lactide-co-glycolide), widely used as a braided surgical sutures; (2) random copolymers comprising about 68 to 75 percent glycolide and about 32 to 25 percent, by weight, ε-caprolactone to form compliant copolymeric monofilaments having a modulus of about 150 to 250 Kpsi, even though no crystallinity was noted to be present in the copolymer as in U.S. Pat. No. 6,494,898 (2002); (3) segmented/block copolymers which are made by two-step synthesis entailing the preparation of a prepolymer containing a minor fraction of glycolate sequences, followed by end-grafting with glycolide or a mixture of monomers containing more than 80 percent glycolide—the respective general type of chain microstructure and composition was used to prepare highly compliant ε-caprolactone/glycolide copolymeric monofilament sutures as in U.S. Pat. No. 4,605,730 (1986), U.S. Pat. No. 4,700,704 (1987), and U.S. Pat. No. 5,133,739 (1992); and (4) segmented block copolymers based on a polyalkylene succinate prepolymer, which is first grafted with trimethylene carbonate and/or ε-caprolactone and then grafted further with glycolide, or a glycolide-rich mixture of monomers, to produce copolymers with minimized hydrolytic stability. Monofilament sutures made of these copolymers were claimed to retain their mechanical properties upon aging in a buffered solution at pH 7.4 and 37° C. for longer periods of time as compared with those based on the caprolactone/glycolide copolymers described in statement numbers 1 and 2. However, monofilament sutures made of the copolymers with minimized hydrolytic instability were shown to exhibit less than optimal modulus to produce compliant medical devices such as the sutures disclosed in U.S. Pat. No. 6,255,408 B1 (2001) and U.S. Pat. No. 6,503,991 (2003). In a successful effort to achieve substantial improvement over the prior art disclosed in U.S. Pat. Nos. 4,605,730, 4,700,704, and 5,133,739, a one-step scheme for the synthesis of crystalline, segmented caprolactone/glycolide copolymers and production of compliant absorbable monofilament sutures therefrom was developed as disclosed in U.S. Pat. No. 6,498,229 (2002). However, the breaking strength retention of the monofilament sutures made of these polymers were less than optimal for a short-term, absorbing suture, and a need for new sutures with optimum strength retention profile, without compromising their exceptional compliance, was ascertained. This and the extremely brief breaking strength profile of the monofilament sutures made of the random copolymer of U.S. Pat. No. 6,494,898 (2002) made the need for novel materials more pressing. Accordingly, this invention deals, in part, with novel, absorbable, high glycolide, ε-caprolactone copolymers with improved hydrolytic stability and breaking strength retention profile over those of U.S Pat. Nos. 6,498,229 and 6,494,898 without compromising the exceptionally low compliance of the polymers subject of those patents. Furthermore, this invention deals with an improvement on the prior art, wherein the novel copolyesters have superior compliance as compared to the polyalkylene succinate-based crystalline copolymer of minimized hydrolytic instability disclosed in U.S. Pat. Nos. 6,255,408 B1 and 6,503,991. Composition limitations associated with the random copolymer approach and process complexity and fair-to-inadequate reproducibility encountered in the two-step synthesis of segmented glycolide copolymer provided the incentive to explore a simple, and yet reliable, approach to prepare crystalline, high glycolide copolymers with a broad range of physicochemical properties and possibly more than one unique functional performance. Extending the concept of one-step synthesis of segmented crystalline glycolide/caprolactone copolymers based on more than about 80 percent glycolide (e.g., 81 to 95 percent) to produce compliant suture materials appears equally challenging. And this evoked exploring the synthesis of these copolymers in a monocentric polyaxial chain configuration to produce relatively more compliant materials than commercially available, high glycolide, low compliance copolymers such as those based on 90 percent glycolide which is used in producing Vicryl® braided sutures.